"Certainly we've won the global currency battle for now," says Brian Kelly of Shelter Harbor Capital. The stronger dollar, he says, "is actually a good thing because money's flowing into the U.S." As for the dollar's pattern of moving in the opposite direction from stocks, "that old correlation seems to have broken, and it's a good thing."

"The U.S. economy right now is the best of a bad bunch," says Amelia Bourdeau, director of foreign exchange at Westpac Institutional Bank. The dollar has been rallying of late because of a flight to quality in the wake of the Italian election and downbeat euro zone economic reports, she told CNBC's Amanda Drury. "However, today it was certainly about the jobs report."

Andrew Busch, publisher of andrewbusch.com, goes a step further, arguing that Friday's report pointed to a "dichotomy out there between the United States and Europe."

So how should you trade the dollar-euro pair now?

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The strong jobs report boosts the dollar. So how high can it go? Is the U.S. winning the global currency war, with CNBC's Melissa Lee and the Money in Motion traders.

Busch is hesitant to sell the euro too aggressively. "We're getting to some levels in the euro where there is going to be support," he says. Also, the jobs report is just one piece of data from before the March 1 sequestration.

But Busch says that markets will continue responding to the strong report, so he does want to sell the euro against the dollar. He cautions that with the euro close to its 200-day moving average, tight stop is key. So he recommends entering the trade at 1.3050, setting a stop at 1.3100 with a target of 1.2850, and adds, "I'm willing to resell if we move down through the 200-day moving average."